Question

limit of 4-sqr.root(x)/ (x-16).... x is appoaching 16

Answer 1

\[\lim_{x\rightarrow 16}\frac{4-\sqrt{x}}{x-16}\]

Answer 2

rationalize the numerator by multiplying top and bottom by
\[4+\sqrt{x}\]

Answer 3

\[\frac{4-\sqrt{x}}{x-16}\times \frac{4+\sqrt{x}}{4+\sqrt{x}}\]
\[=\frac{16-x}{(x-16)(4+\sqrt{x})}\]
\[=\frac{-1}{x+\sqrt{16}}\]

Answer 4

then replace x by 16 to get
\[\frac{-1}{8}\]

Answer 5

this line was a typo
\[=\frac{-1}{x+\sqrt{16}}\] it should have been
\[\frac{-1}{4+\sqrt{x}}\]